From my understanding, in a given linear system represented by $Ax=b$, $A$ is the amount of each vectors, $x$ the vectors making up the system and $b$ the vector that I'm trying to reach through my set of $x$.

If I was given $2$ equations with $ 3$ unknowns then the $b$ I'm trying to reach has $2$ dimensions, which is not representable by a $3d$ vector? On the other hand, if I was given three equations with only two unknowns wouldn't be like trying to reach a $3d$ vector from $2d$ vectors?

Somehow this would give me an infinite set of solutions?



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